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Censored data are frequently found in diverse fields including environmental monitoring, medicine, economics and social sciences. Censoring occurs when observations are available only for a restricted range, e.g., due to a detection limit. Ignoring censoring produces biased estimates and unreliable statistical inference. The aim of this work is to contribute to the modelling of time series of counts under censoring using convolution closed infinitely divisible (CCID) models. The emphasis is on estimation and inference problems, using Bayesian approaches with Approximate Bayesian Computation (ABC) and Gibbs sampler with Data Augmentation (GDA) algorithms.

A curva descrita pelos pares (a, b) no plano tais que a, b > 0, a ≠ b e a^b = b^a é parametrizável pelos declives 0 < t ≠ 1 do feixe de rectas de equações cartesianas y = tx, o que permite descrever facilmente os pontos do traço desta curva cujas coordenadas são ambas números algébricos, ou inteiros algébricos ou racionais. Em particular, uma tal parametrização fornece um método simples de encontrar coordenadas de pontos desta curva que são números transcendentes.

In the Valongo Belt, with an extension of about 90 km, located very close to Porto, northern Portugal, dozens of ore deposits of various metallic minerals and coal were exploited in the 19th and 20th centuries. One of the metals most intensely exploited was antimony, with or without associated gold mineralization. This research intends to verify the extent of the current environmental legacy of ancient antimony mining. A typical old mine was selected. The main objectives were to verify whether the environmental legacy still manifests today, how natural processes contributed to an environmental dispersion of the mining footprint and whether the environmental legacy was absorbed by developments in a new landscape modified by anthropic activities. The topography of the area was captured using a Light Detection and Ranging (LIDAR) based drone system. The regional background was characterized by the geo-referenced chemical analysis of 157 soil samples, collected in a 35 × 35 m grid. The former mining area was characterized by 58 supplementary samples. The mining area is distinct from the background by higher antimony and zinc levels, constituting two distinct populations, as confirmed by statistical tests. In the samples collected in the industrial zone, six elements were considered contaminants: As, Cu, Mo, Sb, Sn and Zn. The concentrations of these elements were statistically examined using multivariate statistical analyses (principal component analysis and correspondence analysis). The main conclusions are: (a) the mining heritage area is discernible from the highly mineralized background; (b) in the mining zone, it is possible to distinguish the processing industrial area from the waste rock storage; (c) the natural processes of environmental dispersion were of little relevance; (d) the environmental legacy was smoothed and mostly incorporated into the new post-industrial landscape created by anthropic activities.

We present a simple proof of the fairly general fact that an invariant right-weak Gibbs probability measure is an equilibrium state, using a generalization of the formula of Brin and Katok for the ...

This paper reports numerical experiments done on a two-parameter family of vector fields which unfold an attracting heteroclinic cycle linking two saddle-foci. We investigated both local and global bifurcations due to symmetry breaking in order to detect either hyperbolic or chaotic dynamics. Although a complete understanding of the corresponding bifurcation diagram and the mechanisms underlying the dynamical changes is still out of reach, using a combination of theoretical tools and computer simulations we have uncovered some complex patterns. We have selected suitable initial conditions to analyze the bifurcation diagrams, and regarding these solutions we have located: (a) an open domain of parameters with regular dynamics; (b) infinitely many parabolic-type curves associated to homoclinic Shilnikov cycles which act as organizing centers; (c) a crisis region related to the destruction or creation of chaotic attractors; (d) a large Lebesgue measure set of parameters where chaotic regimes are dominant, though sinks and chaotic attractors may coexist, and in whose complement we observe shrimps.

A otimização é um ramo da área da matemática e dos métodos numéricos que tem sido objeto de investigação teórica e aplicada ao longo das últimas décadas. Em particular, a engenharia é uma das áreas onde a otimização tem encontrado terreno propício para a sua aplicação e desenvolvimento teórico e prático. As técnicas de otimização alcançaram uma maturidade sem precedentes e são usadas num largo espectro de aplicações industriais em diferentes áreas, nomeadamente engenharia estrutural, aeroespacial, automóvel, química, eletrónica, fabricação assistida por computador e produção industrial. A otimização pode ser definida como o estabelecimento racional de um projeto que é o melhor dentro de todos os possíveis de acordo com um ou mais objetivos predefinidos e obedecendo a um conjunto prescrito de restrições. Em sentido lato, as condições referidas requerem uma integração adequada entre duas áreas bem definidas: a otimização em engenharia e a otimização matemática. Desta interação resulta a integração da otimização no ciclo de projeto de sistemas em engenharia. Para aplicar os conceitos matemáticos à pesquisa do projeto ótimo de sistemas em engenharia, deve-se formular o problema matemático subjacente e construir o respetivo modelo. Para tal, é necessário definir as variáveis de projeto, os objetivos e as restrições do problema de otimização. Neste livro, é feita uma apresentação detalhada sobre os conceitos matemáticos de otimização, bem como a descrição dos principais algoritmos de acordo com a sua taxonomia. Considera-se constituir esta obra um importante contributo para a disseminação do conhecimento nesta área e uma referência fundamental para estudantes, investigadores, cientistas e engenheiros

In this paper a new approach to the Reliability-based Robust Design Optimization (RBRDO) of angle-ply composite laminate structures is presented. The problem is defined as a bi-objective Robust Design Optimization (RDO) problem, with deterministic and probabilistic constraints . Design optimization is considered as the minimization problem of the weight (optimality) and the determinant of the variance-covariance matrix of the response functionals of the system (robustness). Reliability assessment is executed by the Reliability Index Approach (RIA), as an inner cycle. The key concept of this methodology is the exclusive use of evolutionary algorithms with elitist strategy, allowing for global convergence in the two optimization cycles. The RIA problem was reformulated and a set of new evolutionary operators were developed. A numerical example is presented and the results compared with other RBRDO and RDO formulations. Results show that deterministic and probabilistic structural integrity measures are quite sensitive to uncertainty, for multi-component composite structures.

Realistic analysis of structure failures under uncertainties are due to be associated with the use of probabilistic methods. One of the main problems in structural reliability analysis of composite laminate structures is the possible existence of multiple MPP (Most Probable Failure Point). In this work, we propose a numerical inverse technique for the global MPP search as a function of the anisotropy of laminated composites. Therefore, the analysis considers the maximum loading capability of the composite structure for a prescribed reliability level. This is equivalent to solving a target reliability-based design optimization problem. A Bayesian method to estimate the probability of failure based on Monte Carlo simulation provides the validation of the results. The validation process demonstrates that the proposed methodology is adequate to estimate the probability of failure of the laminated composite structures. Furthermore, the paper outlines and discusses the sensitivity of reliability index under maximum loading variability for angle ply composites. (c) 2018, Springer Nature B.V.

In this paper we introduce a notion of measure theoretical entropy for a finitely generated free semigroup action and establish a variational principle when the semigroup is generated by continuous self maps on a compact metric space and has finite topological entropy. In the case of semigroups generated by Ruelle-expanding maps we prove the existence of equilibrium states and describe some of their properties. Of independent interest are the different ways we will present to compute the metric entropy and a characterization of the stationary measures.

In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behaviour and, from the asymptotic properties of these non-converging time averages, we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. These invariants are determined by the quotient of the real parts of the eigenvalues of the equilibria, a linear combination of their imaginary components and also the transition maps between two cross sections on the separatrices., 23 pages, 4 figures

The moduli space of Higgs bundles has two stratifications. The Bialynicki-Birula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises from the Harder-Narasimhan type of the vector bundle underlying a Higgs bundle. While these two stratification coincide in the case of rank two Higgs bundles, this is not the case in higher rank. In this paper we analyze the relation between the two stratifications for the moduli space of rank three Higgs bundles., Comment: 18 pages; v2: extended results to the non-coprime case, other minor corrections, updated references; v3, v4: corrected typos; to appear in Portugaliae Mathematica

We consider a one-parameter family $(f_\lambda)_{\lambda \, \geqslant \, 0}$ of symmetric vector fields on the three-dimensional sphere $\mathbb{S}^3\subset\mathbb{R}^4$ whose flows exhibit a heteroclinic network between two saddle-foci inside a global attracting set. More precisely, when $\lambda = 0$, there is an attracting heteroclinic cycle between the two equilibria which is made of two $1$-dimensional connections together with a $2$-dimensional sphere which is both the stable manifold of one saddle-focus and the unstable manifold of the other. After slightly increasing the parameter while keeping the $1$-dimensional connections unaltered, the two-dimensional invariant manifolds of the equilibria become transversal, and thereby create homoclinic and heteroclinic tangles. It is known that these newborn structures are the source of a countable union of topological horseshoes, which prompt the coexistence of infinitely many sinks and saddle-type invariant sets for many values of $\lambda$. We show that, for every small enough positive parameter $\lambda$, the stable and unstable manifolds of the equilibria and those infinitely many horseshoes are contained in the global attracting set of $f_\lambda$. Moreover, we prove that the horseshoes belong to the heteroclinic class of the equilibria. In addition, we verify that the set of chain-accessible points from either of the saddle-foci is chain-stable and contains the closure of the invariant manifolds of the two equilibria., Comment: 5 figures